Bring 4 cups water and 1 teaspoon salt to boil in heavy medium saucepan. Gradually whisk in polenta. Reduce heat to medium-low. Cook polenta until tender, adding more water as needed if too thick, and whisking frequently, about 20 minutes. Stir in 3 tablespoons butter. Season with salt and pepper. Cover to keep warm.

Reheat mushroom mixture. Melt 2 tablespoons butter in another large skillet over high heat. Add scallops and sauté until just translucent in center, about 1 minute. Stir scallops and juices into mushrooms. Season with salt and pepper.

For best results and flavor, look for dry-packed scallops, which are minimally treated—or untreated—with a phosphate solution (as a preservative). Untreated scallops tend to be beige, whereas treated ones have a milky-white appearance. Specialty fish sellers and Whole Foods Market are good sources.